This is an announcement for the paper "Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane" by Benoit Kloeckner.

Abstract: We prove that a plane domain which is almost isoperimetric (with respect to the $L^1$ metric) is close to a square whose sides are parallel to the coordinates axis. Closeness is measured either by $L^\infty$ Haussdorf distance or Fraenkel asymmetry. In the first case, we determine the extremal domains.

Archive classification: math.FA math.DG

Mathematics Subject Classification: MSC 51M16, 51M25, 49Q20

Remarks: 9 pages

The source file(s), central_square.pstex: 6034 bytes

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0907.4945

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http://arXiv.org/abs/0907.4945

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